Edit Distance in Near-Linear Time: it's a Constant Factor

Alexandr Andoni, Negev Shekel Nosatzki

Abstract: We present an algorithm for approximating the edit distance between two strings of length n in time n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1+ε</sup> , for any , up to a constant factor. Our result completes a research direction set forth in the recent breakthrough paper [1], which showed the first constant-factor approximation algorithm with a (strongly) sub-quadratic running time. The recent results [2], [3] have shown near-linear complexity only under the restriction that the edit distance is close to maximal (equivalently, there is a near-linear additive approximation). In contrast, our algorithm obtains a constant-factor approximation in near-linear running time for any input strings.